Key Takeaways
- • Researchers from Columbia University and a16z Crypto developed a tractable mathematical model quantifying how trading fees impact arbitrage profits against automated market makers (AMMs) and the adverse selection costs borne by liquidity providers.
- • The study establishes that arbitrage profits in fee-bearing environments are approximately equivalent to loss-versus-rebalancing (LVR)—the frictionless benchmark metric—suggesting fees scale down rather than fundamentally alter arbitrage dynamics.
- • The research extends prior work by Milionis et al., providing a general framework for understanding the relationship between fee structures, arbitrageur profitability, and LP losses in decentralized finance protocols.
- • Published initially in February 2023 with updates through July 2025, the paper has achieved 106+ academic citations, indicating significant influence on AMM mechanism design and DeFi risk modeling.
Summary
A collaborative research effort by Jason Milionis, Ciamac C. Moallemi, and Tim Roughgarden—spanning Columbia University's computer science and business faculties alongside a16z Crypto—has produced foundational academic work analyzing the intersection of automated market maker mechanics, trading fees, and arbitrage economics in decentralized finance.
The core research question addresses a critical operational reality in AMM-based markets: how do transaction fees affect the profitability available to arbitrageurs exploiting price discrepancies, and conversely, how do these fee structures protect or expose liquidity providers (LPs) to adverse selection losses? Rather than treating fees as binary friction, the researchers developed a quantitative framework that models fee impact as a continuous variable within arbitrage dynamics.
The paper's principal contribution is establishing that arbitrage profits under fee regimes scale proportionally with the frictionless baseline metric known as loss-versus-rebalancing (LVR). This finding has material implications for protocol designers: it suggests that fee levels can be calibrated to manage arbitrage losses without requiring structural changes to AMM bonding curves or matching algorithms. In effect, fees function as a linear dampener on arbitrage profitability rather than creating non-linear threshold effects.
The work builds methodologically on prior research by Milionis et al., extending the model's applicability across diverse fee structures and market conditions. Since initial publication in February 2023, the research has accumulated 106+ citations across academic literature, reflecting adoption by both cryptographic researchers and institutional practitioners evaluating DeFi infrastructure risks. Subsequent updates through July 2025 indicate ongoing refinement of the model and its applications to evolving AMM architectures.
For institutional investors and family offices evaluating DeFi liquidity provision strategies, this research provides quantitative grounding for fee-setting decisions and LP profitability forecasting—directly informing capital allocation to yield-generating token pools and protocol governance positions.
The core research question addresses a critical operational reality in AMM-based markets: how do transaction fees affect the profitability available to arbitrageurs exploiting price discrepancies, and conversely, how do these fee structures protect or expose liquidity providers (LPs) to adverse selection losses? Rather than treating fees as binary friction, the researchers developed a quantitative framework that models fee impact as a continuous variable within arbitrage dynamics.
The paper's principal contribution is establishing that arbitrage profits under fee regimes scale proportionally with the frictionless baseline metric known as loss-versus-rebalancing (LVR). This finding has material implications for protocol designers: it suggests that fee levels can be calibrated to manage arbitrage losses without requiring structural changes to AMM bonding curves or matching algorithms. In effect, fees function as a linear dampener on arbitrage profitability rather than creating non-linear threshold effects.
The work builds methodologically on prior research by Milionis et al., extending the model's applicability across diverse fee structures and market conditions. Since initial publication in February 2023, the research has accumulated 106+ citations across academic literature, reflecting adoption by both cryptographic researchers and institutional practitioners evaluating DeFi infrastructure risks. Subsequent updates through July 2025 indicate ongoing refinement of the model and its applications to evolving AMM architectures.
For institutional investors and family offices evaluating DeFi liquidity provision strategies, this research provides quantitative grounding for fee-setting decisions and LP profitability forecasting—directly informing capital allocation to yield-generating token pools and protocol governance positions.
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